We confirm recent results about the differences in temperature and magnetic field strength between the umbra of large and small sunspots. Five Stokes I- and V-spectra from the darkest cores of three different umbrae have been analyzed with the inversion code of the radiative transfer equation by Ruiz Cobo & del Toro Iniesta (1992). The run with depth of temperature, magnetic field (strength and inclination) and velocity along the line of sight are obtained. The larger sunspots turn out to be cooler and possesing a larger magnetic field strength, practically throughout the whole atmosphere. Neither significant gradients of the line-of-sight velocity, nor of the magnetic field inclination, are detected in any of the spots analyzed. Two model atmospheres are given corresponding to hot (small) and cool (large) sunspots. The models are, to a large extent, free from effects of penumbral/photospheric stray-light because it is nearly absent in the large spots and because in the small one, where it is important for the Stokes I-profile, only Stokes V is considered to obtain the model atmosphere. These are the first umbral models in the literature for which a simultaneous determination of the magnetic field and thermodynamic stratifications is presented. The implications of these stratifications for the energy transport in sunspot umbrae are discussed.